Estimating Measures of Formation Flow Capacity and Phase Mobility from Pressure Transient Data Under Segregated Oil and Water Flow Conditions

ABSTRACT

A segregated flow mechanism of oil and water usually takes place in the presence of strong gravity forces in subsurface environments, having specific geometrical and petrophysical properties undergoing simultaneous flow of multiphase fluids. The segregated flow of oil and water is modeled as a two-layer reservoir system, based on the observed data. Accurate estimates or measures of the values of phase mobility of oil and water, in addition to the actual flow capacity of the formation are provided. Reliable reservoir characterizations and reserve estimations are provided based on the in-situ conditions of oil and water in the reservoir.

PRIORITY

The present application is a divisional application of and claimspriority to and the benefit of U.S. Non-Provisional application Ser. No.14/613,780, filed Feb. 4, 2015, the entire disclosure of which isincorporated here by reference.

BACKGROUND OF THE INVENTION Field of the Invention

The present invention relates to pressure transient testing of producinghydrocarbon (oil and gas) reservoirs, and more particularly to measuringformation flow capacity and phase mobility from pressure transient dataunder segregated oil and water flow conditions.

Description of the Related Art

Hydrocarbon reservoirs are typically considered to include thosecontaining either oil, gas or both as recoverable hydrocarbons. A waterphase coexists with hydrocarbons in almost all hydrocarbon reservoirs.Even when both oil and water coexist, these are nevertheless referred toas oil reservoirs. In a good oil reservoir, before any production of oilfrom the reservoir begins, an oil phase is the only mobile phase, whilethe water phase is at its residual saturation and is immobile.

As production continues, the water phase starts to break through towardsthe producing wells. As producing time progresses, the amount of waterproduction rate increases, compared to the simultaneously declining oilproduction rate. The relative water-oil production rates are monitoredat individual producing wells and quantified through a parameter knownin the petroleum industry as “water cut ratio.” A water cut ratio,normally expressed in percentage, is defined as the ratio of waterproduction rate to the total production rate (oil and water together) atthe surface conditions. Any prolonged production at a very high watercut ratio might lead to a decision to abandon this producing well, andto drill another supplementary well for oil production in a region ofthe field, uninvaded by water.

In the presence of strong gravity forces in subsurface environments,having specific geometrical and petrophysical properties undergoingsimultaneous flow of multiphase fluids, segregated flow mechanism of oiland water usually takes place. Under this flow mechanism, the heavierfluid, water phase in this case, tends to position itself at the lowerzone of the reservoir, while the lighter fluid, oil phase, positionsitself at the upper zone of the reservoir. A difference in densitybetween the oil and water phases is the main driving force in theprocess of segregating the oil and the water phases. This process isboosted by the low, creeping velocity of fluids in the reservoir. Thesegregated flow mechanism is observed very often in a number of fieldsknown to Applicant, especially in giant carbonate formations, where goodmobility in both the vertical and horizontal directions of the reservoiris present.

Pressure-transient tests can be viewed as experiments that are conductedon producing oil wells to acquire certain information about itsproductivity and to characterize the in-situ properties of itsnear-wellbore reservoir region. Properties derived from such tests, alsoknown as well tests, are very important in evaluating the reservoirproductivity and the accessibility to the hydrocarbon reserves, inaddition to providing ability to understanding and characterizingreservoir rocks and its dynamic behavior under in-situ conditions.

In typical well test operations, pressure and production rates aremeasured as functions of time, usually using high-resolution gauges,located either at surface or downhole. The pressure and rate responsesfrom the well tests are then analyzed and interpreted by identifyingflow regimes using appropriate well and reservoir models. Analyses ofthe data obtained from well tests, called pressure-transient analyses,have become increasingly sophisticated with many numerical andanalytical approaches. Analyses of data from tests under segregated flowof oil and water are not accurate, because the analysis equations arebased on the assumptions of single-phase flow.

The most widely accepted methodology to-date to analyze multiphase flowis what is referred to as the Perrine method or approach (Perrine, R.L., 1956. Analysis of pressure-buildup curves. Drilling and ProductionPractice, API, 482-509). This approach does not consider rigorously thesegregated flow mechanism as encountered in the oil reservoirs in thepresence of water. As the Perrine method considers effective propertiesdue to the reservoir and the fluids under multi-phase conditions, itdoes not have the capability of estimating the true formation capacity.Thus, the Perrine method provides limited information for reservoircharacterization. Al-Khalifa et al. have shown with examples of the waythe Perrine method is utilized in extracting the reservoir parameters(Al-Khalifa, A. J., Home, R. N. and Aziz, K., 1989. Multiphase Well TestAnalysis: Pressure and Pressure-Squared Methods. Paper SPE 18803presented at the SPE California Regional Meeting, Bakersfield,California, April 5-7).

Further, as far as is known, previous efforts (mainly the Perrinemethod) in the prior art treat the multiphase flow systems the same wayirrespective of the specific flow regime in hand. These prior methods donot distinguish the segregated flow mechanism from the other mechanisms.The Perrine method can only extract very limited information, related tothe values of mobility in oil and water phases. It thus does not havethe capability of determining the true formation capacity (or equivalentdry oil flow capacity). This method provides an accurate method ofextracting flow capacity and phase mobility under segregated flow of oiland water.

SUMMARY OF THE INVENTION

Briefly, the present invention provides a new and improved computerimplemented method of determining a measure of oil flow capacity from anoil production zone and water flow capacity from a water production zoneas segregated flow in a layer of a subsurface reservoir based on apressure transient test of the layer. Phase mobility values can beextracted readily from the corresponding flow capacity values. Formationflow parameters for the oil production zone and the water productionzone are obtained. A test measure of well pressure is obtained duringthe pressure transient test of the layer containing both oil and waterat sampled instants of measurement during the pressure transient test ofthe layer. From the measured well pressure, the corresponding pressurederivative at the original sampled instants of measured well pressure iscalculated by utilizing the production rates. An estimated value of oilphase flow capacity of the oil production zone, and an estimated valueof water phase flow capacity of the water production zone aredetermined. In addition, the equivalent oil phase flow capacity of thetested layer is also determined. A model of wellbore flowing pressure ofthe layer is determined based on the test measure of well pressure ofthe layer. A model oil production rate for the layer based on the modelwellbore flowing pressure and the formation flow parameters; and a modelwater production rate for the layer based on the model wellbore flowingpressure and the formation flow parameters is determined. The modelwellbore flowing pressure is compared with the test measure of wellpressure; the model measure of well pressure change is compared with thetest measure of well pressure change; and the model pressure derivativeis compared with the test pressure derivative. If the model measures andtest measures match within an acceptable tolerance, the determinedformation flow parameters of the layer are stored. If not, the formationflow parameters of the layer are adjusted, and the steps of determininga model wellbore flow pressure, determining a model pressure derivative,and the steps of comparing are repeated based on the adjusted formationflow parameters of the layer.

The present invention further provides a new and improved dataprocessing system for determining a measure of oil flow capacity from anoil production zone and water flow capacity from a water production zoneas segregated flow in a layer of a subsurface reservoir based on apressure transient test of the layer. The phase mobility values can alsobe extracted readily from the flow capacity values. The data processingsystem includes a processor which obtains formation flow parameters forthe oil production zone and the water production zone, and also obtainsa test measure of well pressure change during the pressure transienttest of the layer. The processor also obtains a test measure of wellpressure during the pressure transient test of the layer, and then atest pressure change and derivative of well pressure at sampled instantsof measurement during the pressure transient test of the layer arecalculated. The processor determines an estimated value of oil phaseflow capacity of the oil production zone, and an estimated value ofwater phase flow capacity of the water production zone. The processordetermines a model wellbore flowing pressure of the layer based on thetest measure of well pressure of the layer. The processor determines amodel oil production rate for the layer based on the model wellboreflowing pressure and the formation flow parameters, and a model waterproduction rate for the layer based on the model wellbore flowingpressure and the formation flow parameters. The processor compares themodel wellbore flowing pressure with the test measure of well pressure;the model measure of well pressure change with the test measure of wellpressure change; and the model pressure derivative with the testpressure derivative. If the model measures and test measures matchwithin an acceptable tolerance, the processor stores the determinedformation flow parameters of the layer. If not, the processor adjuststhe formation flow parameters of the layer, and repeats the steps ofdetermining a model wellbore flow pressure, determining a model pressurederivative, and comparing based on the adjusted formation flowparameters of the layer.

The present invention further provides a new and improved data storagedevice which has stored in a non-transitory computer readable mediumcomputer operable instructions for causing a data processing system todetermine a measure of oil flow rate from an oil production zone andwater flow rate from a water production zone as segregated flow in alayer of a subsurface reservoir based on a pressure transient test ofthe layer. The instructions stored in the data storage device causingthe data processing system to perform steps of obtaining formation flowparameters for the oil production zone and the water production zone,and obtaining a test measure of well pressure during the pressuretransient test of the layer. The instructions also cause the dataprocessing system to perform steps of calculating a test measure of wellpressure during the pressure transient test of the layer, andcalculating a test pressure derivative of well pressure at sampledinstants of measurement during the pressure transient test of the layer.The instructions cause the data processing system to determine anestimated value of oil phase flow capacity of the oil production zone,and an estimated value of water phase flow capacity of the waterproduction zone and the equivalent oil phase flow capacity of the testedlayer. The corresponding mobility from the calculated flow capacity isreadily obtained by dividing the flow capacity by the corresponding paythickness and the fluid viscosity. The instructions also cause the dataprocessing system to determine a model wellbore flowing pressure of thelayer based on the test measure of well pressure of the layer, determinea model oil production rate for the layer based on the model wellboreflowing pressure and the formation flow parameters, and determine amodel water production rate for the layer based on the model wellboreflowing pressure and the formation flow parameters. The instructionscause the data processing system to compare the model wellbore flowingpressure with the test measure of well pressure, compare the modelmeasure of well pressure change with the test measure of well pressurechange, and compare the model pressure derivative with the test pressurederivative. If the model pressure measures and test pressure measuresmatch within an acceptable tolerance, the instructions cause the dataprocessing system to store the determined formation flow parameters ofthe layer with the formation and phase flow capacity values. If not, theinstructions cause the data processing system to adjust the formationflow parameters of the layer, and repeat the steps of determining amodel wellbore flow pressure, determining a model pressure derivative,and comparing based on the adjusted formation flow parameters of thelayer.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view, taken in cross-section, of a producing wellin the earth with segregated flow of oil and water phases from aformation layer.

FIG. 2 is a functional block diagram of a flow chart of data processingsteps for obtaining estimated measures of formation flow capacity andphase mobility according to the present invention.

FIG. 3 is a schematic diagram of a data processing system for obtainingestimated measures of formation flow capacity and phase mobility frompressure transient data according to the present invention.

FIG. 4 is a log-log plot showing an example of the pressure drop andpressure derivative data from a producing well in the earth in withsegregated flow of oil and water phases.

FIG. 5 an example of history plot of flowing bottom-hole pressure at awell obtained from a case study (pressure transient test) to be used forestimated measures of formation flow capacity and phase mobilityaccording to the present invention.

FIG. 6 is an example plot of individual oil and water phase rates andtotal production rate obtained from a case study (pressure transienttest) forming estimated measures of formation flow capacity and phasemobility according to the present invention.

FIG. 7 is a log-log plot of pressure drop and pressure derivatives forthe same case study (pressure transient test) as that of FIGS. 5 and 6.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In the drawings, FIG. 1 represents schematically a cross-sectional viewof a subsurface reservoir R into which a vertical hydrocarbon producingwell 10 in a wellbore 12 which has been drilled extending into a poroussubsurface formation producing layer 14 between two impermeable rocklayers 16 and 18. As shown in FIG. 1 at 20, an oil phase is present inan oil zone 22 of height h_(o) in the porous producing layer 14, and awater phase 24 is present in a water zone 25 of height h_(w) in layer14. The well 10 is completed in the layer 14 at a sandface 27 with acasing string 26.

From well-log measurements, it is possible to confirm the location of asharp interface 28 between the oil phase 20 and the water phase 24 inthe reservoir layer 14. During segregated flow, above the interface 28,only the oil phase 20 is mobile, while the water phase is present inirreducible water saturation which is immobile. In contrast, below theinterface 28, only the water phase 24 moves, while the oil phase istrapped in residual oil saturation and stays immobile. Only the mobilefluid in a particular zone contributes to the production through thewellbore, and the immobile fluid in that zone stays in the reservoir.The segregated flow of oil and water is governed by certain dynamicparameters of the formation (e.g., relative permeability, absolutevalues of vertical and horizontal permeability), petrophysicalparameters (e.g., porosity, oil and water zone thicknesses), and certaincharacteristics parameters related to the fluids in place (e.g., densitydeference and average fluid velocity).

Understanding the fundamentals of multiphase flow and the underlyingmechanism is essential in proper management of oil fields. Among thevery few multiphase flow mechanisms encountered at reservoir conditions,segregated flow of oil and water phases is the most frequent one.Segregated flow takes place primarily as a result of the densitydifference between the oil and water phases. Generally, fluid flowsthrough porous media at relatively low velocity permitting gravity toforce fluids to segregate from each other, where heavier fluids (e.g.,water) slump down to the base of the reservoir and lighter fluids (e.g.,oil) rise up. The segregated flow mechanism is commonly observed in mostoil fields and can be identified by having a sharp interface between theoil and water phases.

Sharp interfaces such as shown schematically at 28 between oil and waterin partially-flooded (with water) regions are repeatedly observed fromwell-logs and other types of measurements in most giant oil fields knownto Applicant. Many pressure-transient tests are run in wells havingsignificant water productions. Analyzing pressure-transient data undersegregated flow conditions using conventional multiphase flow methodsthat are currently employed in the industry is not adequate and couldresult in inaccurate values of the formation flow capacity and theindividual phase mobility.

To overcome this shortcoming, the present invention provides amethodology of analyzing and determining measures the segregated flow ofoil and water as a two-layer reservoir system as shown in FIG. 1. Assuch, the segregated flow parameters can be derived analytically. Havinghonored the in-situ physics, the present invention provides betterestimates of the formation flow capacity and the oil and water phasemobility. As has been mentioned, so far as is known, current approachesto analysis of well test data under segregated flow conditions of oiland water are inadequate in capturing the underlying physics.

Under conditions of multiphase flow, the oil and water phases 20 and 24approach the vertical well 10 separately. The oil phase 20 is producedseparately from a clear, distinguished oil zone 22 of layer 14 withdistinct static and dynamic flow related properties as shown in FIG. 1(e.g., thickness h_(o), permeability k_(oz), porosity ϕ_(oz), totalcompressibility c_(to), residual water saturation S_(wirr) and relativepermeability of oil k _(ro) at residual water saturation). Similarly,the water phase 24 is produced from a well-defined water zone 26 locatedat the bottom of the reservoir layer 14, having distinct static anddynamic flow related properties (e.g., thickness h_(w), permeabilityk_(wz), porosity ϕ_(wz), total compressibility c_(tw), residual oilsaturation S_(orw) and relative permeability of water k _(rw) atresidual oil saturation). Each of zones 22 and 26 thus has its ownproperties as porosity, permeability, total compressibility and residualsaturation fractions. After leaving the sandface 25 of the well to beproduced, the oil and water are mixed in the wellbore 12 as the phasestravel towards the wellhead at surface. The mixture is produced andmeasured at surface and the water cut ratio, or fraction of water in thetotal mixture is determined.

The present invention provides measures of the formation flow capacityand phase mobility of the two distinct layers of oil and water around avertical producing well, as shown in in FIG. 1. The distinctness of thelayers is dealt with through letting the reservoir and fluid propertiesin each layer be allowed to have its own distinct values for the sake ofgenerality. Production logs and well tests are popular tools in the oilfields to recognize such segregated conditions. The present inventiontreats the problem as a two-layer reservoir system with no crossflow ofoil and water between the layers. The analytical solution provided withthe present invention considers a constant value to the total rate ofproduction of oil and water during the production (or drawdown) periodof the pressure-transient test. The present invention is applicable tothose reservoirs where both oil and water phases are present, but nofree gas phase is available at reservoir conditions.

Set forth below are nomenclature and working equations according to themethodology of the analytical solution, also interchangeably referred toas the model, which is provided with the present invention tocharacterize the formation flow capacity and the values of multiphasemobility under segregated flow conditions.

Nomenclature

-   C Wellbore storage constant, bbl/psi-   c_(o), c_(w) Compressibility of oil and water phases, respectively,    psi⁻¹-   c_(r) Formation compressibility, psi⁻¹-   c_(to), c_(tw) Total compressibility in oil and water zones,    respectively, psi⁻¹-   f_(w) Fractional flow of water, fraction-   H Total reservoir thickness of oil and water layers, (h_(o)+h_(w)),    ft-   h_(o), h_(w) Thicknesses of the oil and water zones, respectively,    ft-   k_(oz), k_(wz) Absolute permeability in oil and water zones,    respectively, md-   k _(ro) Relative permeability of oil at irreducible water    saturations, fraction-   k _(rw) Relative permeability of water at residual oil saturations,    fraction-   K₀( ), K₁ ( ) Modified Bessel function of the second kind of orders    0 and 1, respectively-   l Laplace transform parameter, hr⁻¹-   pi Initial reservoir pressure, psia-   p _(wf) Flowing bottom-hole pressure in Laplace domain, psia-hr-   q_(o) Oil production rate at surface conditions, STB/d-   q_(t) Total liquid production rate at reservoir conditions, bbl/d-   q_(w) Water production rate at surface conditions, STB/d-   q_(o)B_(o) Oil production rate at reservoir conditions in Laplace    domain, bbl-hr/d-   q_(w)B_(w) Water production rate at reservoir conditions in Laplace    domain, bbl-hr/d-   r_(w) Physical wellbore radius, ft-   {umlaut over (r)}_(w) _(o) Equivalent wellbore radius in oil zone    calculated using Equation 14, ft-   {umlaut over (r)}_(w) _(w) Equivalent wellbore radius in water zone    calculated using Equation 15, ft-   S_(orw) Residual oil saturation in the water zone, fraction-   s_(o), s_(w) Skin factors in oil and water zones, respectively,    dimensionless-   S_(wirr) Irreducible water saturation in the oil zone, fraction-   t Elapsed time, hr-   σ_(o), σ_(w) Parameters calculated using Equations 6 and 7 for oil    and water phases, respectively

$\left( \frac{cP}{{md} - {psia} - {hr}} \right)^{1/2}$

-   η_(o), η_(w) Diffusivity parameters for oil and water zones    calculated using Equations 8 and 9, respectively, md-psia-cP⁻¹-   ξ_(o), ξ_(w) Parameters calculated using Equations 10 and 11 for oil    and water phases, respectively,

${ft}^{2} - \left( \frac{md}{{psia} - {hr} - {cP}} \right)^{1/2}$

-   ϕ_(oz), ϕ_(wz) Porosity in oil and water zones, respectively,    fraction-   μ_(o), μ_(w) Viscosity of oil and water phases, respectively, cP

Once the oil and water phases leave the sandface 25 and enter theborehole through the completed interval(s), the flowing bottom-holepressures of both phases are considered for the purposes of the presentinvention to be equal at any given depth inside the wellbore 12 due to aminor difference in hydrostatic pressure at the respective mid-point ofoil and water layers. In normal practice, flowing bottom-hole pressureis measured at a depth inside the wellbore, where the gauges arelocated, which are later corrected to a datum depth. Thus, at the gaugedepth, oil and water phase pressures are considered identical. Thiscondition can be expressed mathematically as a function of time asfollows:

p _(wf)(r _(w) ,t)=p _(w)({umlaut over (r)} _(w) _(w) ,t)=p _(o)({umlautover (r)} _(w) _(o) ,t)  (1)

where p_(wf) is the flowing bottom-hole pressure of the mixture of oiland water in psia, p_(w) is the flowing bottom-hole pressure of thewater phase alone in psia, p_(o) is the flowing bottom-hole pressure ofthe oil phase in psia, t is the time in hr, r_(w) is the actual wellboreradius, {umlaut over (r)}_(w) _(w) is the effective wellbore radius inft in the water zone and {umlaut over (r)}_(w) _(o) is the effectivewellbore radius in ft in the oil zone. In the presence of skin factors,the physical wellbore radii are corrected for the effective wellboreradii.

Equation (1) states that the bottom-hole flowing pressure at any giventime equals the pressure of the water phase 24 just leaving the waterzone 26 and the pressure of the oil phase 20 just leaving the oil zone22 at a particular time. In other words, the oil and water pressures areevaluated at the sandface since the pressure of the mixture at any pointin a cross section of the wellbore is considered identical for allpractical purposes. The effective wellbore radius, as will be definedwith equations later, is used to account for the skin effects at the oiland water zones 22 and 26. For generalization purposes, the modelprovided according to the present invention can handle different skinfactors at each of the separate zones of oil and water, although, thismight be difficult to confirm such cases in reality.

Since the formulation is based on a constant total production rate,q_(t), the flowing wellbore pressure, p_(wf), changes as a function oftime. In the mathematical model, the total production rate, q_(t), atthe reservoir conditions, is considered constant, while individual phaserates, q_(o) and q_(w), are allowed to change with time. The flow ratemodel with the rates at reservoir conditions is expressed as:

q _(t) =q _(o)(t)B _(o) +q _(w)(t)B _(w)  (2)

In Equation 2, q_(t) is at reservoir conditions in bbl/d, while q_(o)and q_(w) are at standard conditions in STB/d. The oil and waterformation volume factors, B_(o) and B_(w), which are used to convert oiland water production rates from surface conditions to reservoirconditions as both B_(o) and B_(w) have the units of bbl/STB.

Presentation of the Model

The equations expressing the physical relationships of segregated oiland flow are expressed below. The model is based on the derived from theanalytical solution of the known diffusivity equation that describespressure as a continuous function of space and time in porous media. Allequations are presented in the system of US Oilfield units. Conversionsto any other system of units may be readily performed and iscontemplated with the present invention.

The effects of wellbore storage and skin are included through the use ofwellbore storage constant, C, in bbl/psi, and the effective wellboreradius, respectively, as indicated previously. All pressures, includingthose in the oil and water zones, are in psia and are corrected to adatum depth.

The model permits determination of the flowing bottom-hole pressure.Individual phase rates (oil and water) are also determined with themodel to verify the input phase rates and to optimize the inputparameters, as may be needed later on. As was previously indicated, themodel considers producing at a constant total production rate, while thepressures, the pressure derivatives and the oil and water productionrates are calculated as a function of time.

The time-dependent quantities (pressure, pressure derivative andindividual phase rates) are presented in the Laplace domain because theoriginal partial differential equations are solvable in this domain. Theparameters that are calculated in the Laplace domain are presented witha bar on top of them (e.g. p _(wf), q_(o)B_(o) , and q_(w)B_(w) ). Aninversion to the real time domain is required to obtain the desiredsolution. This step can be achieved numerically using what is called theStehfest algorithm [Stehfest, H., 1970, Algorithm 368: NumericalInversion of Laplace Transforms. Communications of ACM 13(1):47-49]. TheNomenclature section set forth above provides definitions for thesymbols used in the equations.

Flowing Bottom-Hole Pressure:

$\begin{matrix}{{{\overset{\_}{p}}_{wf}(l)} = {\frac{p_{i}}{l} - \frac{q_{t}{K_{0}\left( {\sigma_{w}{\overset{¨}{r}}_{w_{w}}} \right)}{K_{0}\left( {\sigma_{o}{\overset{¨}{r}}_{w_{o}}} \right)}}{l\begin{bmatrix}{{\xi_{o}{K_{1}\left( {\sigma_{o}r_{w}} \right)}{K_{0}\left( {\sigma_{w}{\overset{¨}{r}}_{w_{w}}} \right)}} + {\xi_{w}{K_{1}\left( {\sigma_{w}r_{w}} \right)}{K_{0}\left( {\sigma_{o}{\overset{¨}{r}}_{w_{o}}} \right)}} +} \\{24\; C\; {{lK}_{0}\left( {\sigma_{w}{\overset{¨}{r}}_{w_{w}}} \right)}{K_{0}\left( {\sigma_{o}{\overset{¨}{r}}_{w_{o}}} \right)}}\end{bmatrix}}}} & (3)\end{matrix}$

Oil Production Rate:

$\begin{matrix}{{\overset{\_}{q_{o}B_{o}}(l)} = \frac{\xi_{o}q_{t}{K_{1}\left( {\sigma_{o}r_{w}} \right)}{K_{0}\left( {\sigma_{w}{\overset{¨}{r}}_{w_{w}}} \right)}}{l\begin{bmatrix}{{\xi_{o}{K_{1}\left( {\sigma_{o}r_{w}} \right)}{K_{0}\left( {\sigma_{w}{\overset{¨}{r}}_{w_{w}}} \right)}} + {\xi_{w}{K_{1}\left( {\sigma_{w}r_{w}} \right)}{K_{0}\left( {\sigma_{o}{\overset{¨}{r}}_{w_{o}}} \right)}} +} \\{24\; C\; {{lK}_{0}\left( {\sigma_{w}{\overset{¨}{r}}_{w_{w}}} \right)}{K_{0}\left( {\sigma_{o}{\overset{¨}{r}}_{w_{o}}} \right)}}\end{bmatrix}}} & (4)\end{matrix}$

Water Production Rate:

$\begin{matrix}{{\overset{\_}{q_{w}B_{w}}(l)} = \frac{\xi_{w}q_{t}{K_{1}\left( {\sigma_{w}r_{w}} \right)}{K_{0}\left( {\sigma_{o}{\overset{¨}{r}}_{w_{o}}} \right)}}{l\begin{bmatrix}{{\xi_{o}{K_{1}\left( {\sigma_{o}r_{w}} \right)}{K_{0}\left( {\sigma_{w}{\overset{¨}{r}}_{w_{w}}} \right)}} + {\xi_{w}{K_{1}\left( {\sigma_{w}r_{w}} \right)}{K_{0}\left( {\sigma_{o}{\overset{¨}{r}}_{w_{o}}} \right)}} +} \\{24\; C\; {{lK}_{0}\left( {\sigma_{w}{\overset{¨}{r}}_{w_{w}}} \right)}{K_{0}\left( {\sigma_{o}{\overset{¨}{r}}_{w_{o}}} \right)}}\end{bmatrix}}} & (5)\end{matrix}$

Parameters Requiring Pre-Calculation for Equation 3, 4 and 5:

$\begin{matrix}{\sigma_{o} = \sqrt{l/\eta_{o}}} & (6) \\{\sigma_{w} = \sqrt{l/\eta_{w}}} & (7) \\{\eta_{o} = \frac{0.0002637\mspace{11mu} k_{o\; z}{\overset{\_}{k}}_{ro}}{\varphi_{o\; z}\mu_{o}c_{to}}} & (8) \\{\eta_{w} = \frac{0.0002637\mspace{11mu} k_{wz}{\overset{\_}{k}}_{rw}}{\varphi_{wz}\mu_{w}c_{tw}}} & (9) \\{\xi_{o} = \frac{k_{o\; z}{\overset{\_}{k}}_{ro}h_{o}\sigma_{o}r_{w}}{141.2\mu_{o}}} & (10) \\{\xi_{w} = \frac{k_{w\; z}{\overset{\_}{k}}_{rw}h_{w}\sigma_{w}r_{w}}{141.2\mu_{w}}} & (11) \\{c_{to} = {c_{r} + {\left( {1 - S_{wirr}} \right)c_{o}} + {S_{wirr}c_{w}}}} & (12) \\{c_{tw} = {c_{r} + {\left( {1 - S_{orw}} \right)c_{w}} + {S_{orw}c_{o}}}} & (13) \\{{\overset{¨}{r}}_{w_{o}} = {r_{w}{\exp \left( {- s_{o}} \right)}}} & (14) \\{{\overset{¨}{r}}_{w_{w}} = {r_{w}{\exp \left( {- s_{w}} \right)}}} & (15)\end{matrix}$

As mentioned earlier, the solution presented with Equations (3), (4),and (5) has been expressed in the Laplace domain, and an inversion of tothe actual time domain is required at step 40 in FIG. 2. This inversionis done numerically using the Stehfest algorithm (1970). A personskilled in the art can readily perform such an inversion withoutdifficulty.

The calculation of pressure derivative

$\left( {t\frac{{dp}_{wf}}{dt}} \right)$

is done simultaneously with the calculation of p_(wf) before applyingthe Stehfest algorithm at step 40 in FIG. 2. Equations (4) and (5) areused mainly to validate the individual phase rates input to the model.The formulation is for unbounded, infinite-acting reservoirs. Averagefluid saturations in the drainage area are assumed to be fixed duringthe test period. In addition, no crossflow of oil and water between thetwo adjacent layers occurs, and capillary pressure (pressure differencebetween the oil and water phases inside the porous media due tointerfacial tension) at the boundary between the oil and water phases isignored.

In order to make use of Equation (3) in determining p _(wf), thethicknesses of the oil, h_(o), and the water, h_(w), zones must beavailable beforehand. Hence this matter is related to step 36 in FIG. 2.In presence of valid production logs, such information can be estimatedwith a reasonable accuracy. In most cases, however, production logs maynot be available, and only total reservoir thickness, H, is availablefrom the formation analysis logs. Under these circumstances, the stepsdescribed to this point are used to extract the oil water zonethicknesses. Fortunately, under segregated flow conditions the thicknessof the oil and water zones can be estimated from the definition offractional flow of water, f_(w), utilizing the individual phaseproduction rates, fluid properties and some petrophysical parameters ofeach zone. Thus, one may use this alternative route in estimating thethicknesses of the oil and water zones when the production logs are notavailable. This is illustrated below through Equations (16) through(18), starting with the definition of fractional flow of water underreservoir conditions as:

$\begin{matrix}{f_{w} = \frac{q_{w}B_{w}}{{q_{w}B_{w}} + {q_{o}B_{o}}}} & (16)\end{matrix}$

Assuming steady-state multiphase flow conditions, the thicknesses of theoil and water phases, h_(w) and h_(o), can be calculated, using thefollowing mathematical expressions, respectively,

$\begin{matrix}{h_{w} = \frac{H}{{\frac{k_{wz}{\overset{\_}{k}}_{rw}\mu_{o}}{k_{o\; z}{\overset{\_}{k}}_{ro}\mu_{w}}\left( {\frac{1}{f_{w}} - 1} \right)} + 1}} & (17)\end{matrix}$h _(o) =H−h _(w)  (18)

Similarly, average water and oil saturation fractions in the testedzones can be estimated, using the following mathematical expressions,respectively:

$\begin{matrix}{S_{w} = \frac{{\varphi_{wz}{h_{w}\left( {1 - S_{orw}} \right)}} + {\varphi_{o\; z}h_{o}S_{wirr}}}{{\varphi_{wz}h_{w}} + {\varphi_{o\; z}h_{o}}}} & (19) \\{S_{o} = \frac{{\varphi_{o\; z}{h_{o}\left( {1 - S_{wirr}} \right)}} + {\varphi_{wz}h_{w}S_{orw}}}{{\varphi_{wz}h_{w}} + {\varphi_{o\; z}h_{o}}}} & (20)\end{matrix}$

A complete process of implementation of this invention with thegenerated model results, utilizing the above equations, is presented inFIG. 2. The purpose of having the model results is to generate modelreservoir responses to compare with those captured from actual welltests. Efforts are made to extract reasonable reservoir parameters,including wellbore storage constant and skin factor, for which there isa good match between the test data and the model results. As will bedescribed below, comparisons are made between test data and determinedmodel values. Once a satisfactory match is obtained between the modelvalues and the measured pressure-transient data, the flow capacity foroil and water phases and the equivalent oil phase (assuming producing atdry-oil conditions) are calculated as:

Flow capacity for oil phase=k _(oz) k _(ro) h _(o)  (21)

Flow capacity for water phase=k _(wz) k _(rw) h _(w)  (22)

Equivalent oil phase flow capacity= k _(ro)(k _(oz) h _(o) +k _(wz) h_(w))  (23)

A computer implemented process according to the present invention ofdetermining measures of formation flow capacity and phase mobility.Individual phase mobility is obtained by dividing the phase flowcapacity by the zone thickness and by the phase viscosity. As this stepis straightforward, extracting the phase flow capacity is important withthe present invention. Under segregated oil and water flow conditions,for pressure transient-test data, an iterative scheme is illustratedschematically in a flow chart F in FIG. 2.

The flow chart F (FIG. 2) illustrates the structure of the logic of thepresent invention as embodied in computer program software. Thoseskilled in the art will appreciate that the flow charts illustrate thestructures of computer program code elements including logic circuits onan integrated circuit that function according to this invention.Manifestly, the invention is practiced in its essential embodiment by amachine component that renders the program code elements in a form thatinstructs a digital processing apparatus (that is, a computer) toperform a sequence of data transformation or processing stepscorresponding to those shown.

As shown at step 30, processing according to the present inventionbegins with a time range being selected from the pressure and time dataobtained during pressure transient test of a layer of interest such asporous subsurface formation producing layer 14 (FIG. 1). The model andits structure have been described above in terms of equations in theLaplace domain. During step 32 in FIG. 2, the measured well pressurep_(wf) and pressure derivative

$\left( {t\frac{{dp}_{wf}}{dt}} \right)$

are formatted in a form for storage and subsequent display in log-logplots, and are available for output display by data processing system D(FIG. 4) in such format.

During step 36 (FIG. 1), relevant petrophysical, reservoir and for bothoil and water zones 22 and 26, together with the properties of thefluids-in-place are gathered. Information, such as porosity and overallnet pay thickness, can be extracted from the interpretation of open-holelogs. Residual fluid saturations and relative permeability end-pointscan be determined from core analyses and laboratory reports onrepresentative rock samples. Individual zone thicknesses can beestimated from production logs, open-hole logs, and/or production data.In the absence of such logs, the alternative method described above withEquations (16), (17) and (18) may be used during step 36 to estimate thezone thicknesses h_(o) and h_(w). Formation volume factor, viscosity andother fluid properties can be determined from fluid properties reportsand correlations.

During step 38 an initial measure or estimate is made of the oil andwater phase flow and the equivalent oil phase d according to Equations(21), (22) and (23) above.

During step 40, model values of well flowing pressure (p_(wf)), and oilflow rate (q_(o)B_(o)) and water flow rate (q_(w)B_(w)) are determinedusing the methodology described with Equations (3) through (15) and theStehfest algorithm mentioned above. The pressure derivative

$\left( {t\frac{{dp}_{wf}}{dt}} \right)$

of the model well pressure p_(wf) and the change in model well pressureare also determined during step 40 in the manner described above. Therespective change in pressure and derivative (log-log) plots are madeready to compare with the actual pressure and derivative of data fromactual transient tests. The data values determined during step 40 areformatted in a form for storage and subsequent display in log-log plots,and are available in that format for output display as indicated at step42 by data processing system D.

During step 44, the model values of well pressure p_(wf), change inpressure and the corresponding pressure derivative

$\left( {t\frac{{dp}_{wf}}{dt}} \right),$

determined during step 40, are compared visually or graphically to thecorresponding measured values, obtained during step 32. The workingequations for the model have been presented above.

Thus, during step 44 the model well pressure change and thecorresponding pressure derivative

$\left( {t\frac{{dp}_{wf}}{dt}} \right)$

responses are compared visually or graphically with the correspondingmeasured data on a log-log plot. Graphical or visual comparisons arerequired for each of well pressure, pressure changes (drawdowns) andpressure derivative during step 44. It is required to compare thepressure values in the same way. The model has been presented earlier interms of equations in the Laplace domain. Thus, the determined modelresults of step 40 are compared to the corresponding test measuredvalues in step 44. If as indicated by step 46 the model values ofpressure obtained during step 40, which are also compared visually orgraphically during step 44, indicate that the model values of pressurebeing compared correspond within a specified acceptable tolerance of themeasured values of test pressure, the model built with the formationflow parameters of the layer is acceptable. Thus, step 46 is aquantitative comparison between the model pressure values and themeasured pressure values. It is a common practice in the industry toleave out the criteria of selecting the closeness between the measuredand the model values with the analyst. Such a process involvesminimizing the standard deviation between the measured pressures and themodel pressures to a preset tolerance (for example, 0.1 psia). As thetolerance value is preset to a lower value, the computational burdenincreases. Once such a preset tolerance is satisfied in step 46, peopleskilled in the art will be pleased to call the model as the reasonablywell matched one.

As indicated at step 48 and 50, once a reasonable match has been foundbetween the model and the test data in steps 40 and 44, the determinedoil flow capacity and water flow capacity and the equivalent oil phaseflow capacity determined during step 40 are stored and displayed withthe data processing system D (FIG. 4). The determined values of the flowcapacity become characteristic parameters determined for the poroussubsurface formation producing layer 14 according to the presentinvention.

Once a satisfactory match is achieved, individual phase flow capacityand equivalent oil phase flow capacity can be calculated using Equations(21), (22), and (23). Phase mobility can also be extracted from the flowcapacity. Average saturation fractions of oil and water in the testedlayers can also be estimated using Equations (19) and (20). Thesenumbers are very important to reservoir engineers in estimatingremaining oil reserves.

If the outcome of step 46 indicates that the model pressure values donot fall within an acceptable tolerance of the measured pressure values,the values of the formation flow parameters are adjusted during step 52to seek for a better match between the model pressure values and themeasured pressure values. Processing returns to step 40 for processingbased on the adjusted values of formation parameters. Processingcontinues for further iterations until during step 46, an acceptablematch between the model pressure values and the measured test valuesresults due to a set of adjusted values of formation parameters in step52.

As illustrated in FIG. 3, the data processing system D includes acomputer 60 having a processor 62 and memory 64 coupled to the processor62 to store operating instructions, control information and databaserecords therein. The data processing system D may be a multicoreprocessor with nodes such as those from Intel Corporation or AdvancedMicro Devices (AMD), an HPC Linux cluster computer or a mainframecomputer of any conventional type of suitable processing capacity suchas those available from International Business Machines (IBM) of Armonk,N.Y. or other source. The data processing system D may also be acomputer of any conventional type of suitable processing capacity, suchas a personal computer, laptop computer, or any other suitableprocessing apparatus. It should thus be understood that a number ofcommercially available data processing systems and types of computersmay be used for this purpose.

The processor 62 is, however, typically in the form of a personalcomputer having a user interface 66 and an output display 68 fordisplaying output data or records of processing of measurementsperformed according to the present invention. The output display 68includes components such as a printer and an output display screencapable of providing printed output information or visible displays inthe form of graphs, data sheets, graphical images, data plots and thelike as output records or images.

The user interface 66 of computer 60 also includes a suitable user inputdevice or input/output control unit 70 to provide a user access tocontrol or access information and database records and operate thecomputer 60.

Data processing system D further includes a database 74 stored inmemory, which may be internal memory 64, or an external, networked, ornon-networked memory as indicated at 76 in an associated database server78. The database 74 also contains various data including the time andpressure data obtained during pressure transient testing of the layerunder analysis, as well as the rock, fluid and geometric properties oflayer 14, and the casing, annulus and other formation properties,physical constants, parameters, data measurements identified above withrespect to FIG. 1 and the Nomenclature table.

The data processing system D includes program code 80 stored in a datastorage device, such as memory 64 of the computer 60. The program code80, according to the present invention is in the form of computeroperable instructions causing the data processor 62 to perform themethodology of determining measures of formation flow capacity and phasemobility from pressure transient data under segregated oil and waterflow conditions.

It should be noted that program code 80 may be in the form of microcode,programs, routines, or symbolic computer operable languages that providea specific set of ordered operations that control the functioning of thedata processing system D and direct its operation. The instructions ofprogram code 80 may be stored in non-transitory memory 64 of thecomputer 60, or on computer diskette, magnetic tape, conventional harddisk drive, electronic read-only memory, optical storage device, orother appropriate data storage device having a computer usable mediumstored thereon. Program code 80 may also be contained on a data storagedevice such as server 68 as a non-transitory computer readable medium,as shown.

The processor 62 of the computer 60 accesses the pressure transienttesting data and other input data measurements as described above toperform the logic of the present invention, which may be executed by theprocessor 62 as a series of computer-executable instructions. The storedcomputer operable instructions cause the data processor computer 60 todetermine of formation flow capacity and phase mobility from pressuretransient data under segregated oil and water flow conditions in themanner described above and shown in FIG. 2. Results of such processingare then available on output display 68. The set of FIGS. 5, 6 and 7 isan example display of such result.

The inventors have observed in their numerical experiments that thepresent invention methodology in determining segregated flow arrives ata unique value for the phase flow capacity even with differentcombinations of formation flow parameters h_(o), h_(w), k _(ro) and k_(rw) at a fixed total flow capacity. It is to be noted that all theequations presented herein are valid for a constant total rate ofproduction, q_(t), while the well is producing (or during a period ofdrawdown). These equations can also be utilized under variable rates ofproduction, including during buildup periods (the well is shut-infollowing a period of flow or drawdown) by applying the principle ofsuperposition, which is a commonplace in the industry The presentinvention is thus readily applicable in cases of variable rates ofproduction, including buildup periods.

Diagnostic Plots

Diagnostic plots such as an example shown in FIG. 4 are used repeatedlyin pressure-transient well test interpretations. These provide veryrigorous tools in analyzing raw data and for identifying flow regimesfor estimating the key reservoir parameters. Diagnostic plots aregenerated by plotting pressure drop, pressure difference or pressuredrawdown (initial pressure minus bottom-hole flowing pressure) andpressure derivative as a function of time on log-log scale. Thesegregated flow model does not provide any distinct feature in thelog-log plot other than the conventional pressure derivative plot forvertical-well model. Although built with the segregated flow model, itis to be recognized that FIG. 4 depicts a typical diagnostic plot for avertical well model in a homogenous, infinite-acting, reservoir.However, the extended computations for extracting flow capacity andmobility with the help of the associated model make this inventionworthwhile under segregated flow of oil and water in petroleumreservoirs. Once the radial flow regime is identified on a diagnosticplot (indicated by stabilization of the pressure derivative curve atlater times to the level of the reservoir transmissibility line), thetotal flow capacity and phase mobility of the system can be determinedwith the present invention.

In addition, knowledge of the individual phase rates with the presentinvention allows for the calculation of the flow capacity of the waterand oil phases, separately. The following case study is presented, ofwhich the input parameters to the segregated flow model are listed inTable 1 below. The well has been set to produce at a constant productionrate for 500 hr before shutting in the well for a period of 500 hr. Theflowing bottom-hole pressure values are computed, using Equation (3),following the required inversion to the time domain using the Stehfestalgorithm (1970). The principle of superposition in time has been usedto compute pressure data during the shut in (buildup) period, which is aconventional practice utilized by those skilled in the art.

As no production logs have been available in this case, the individualphase rates, q_(o) and q_(w), have been used to calculate the zonethicknesses, h_(o) and h_(w), using Equations (16), (17) and (18). Thevalues of h_(o) and h_(w) are 50 and 100 ft, respectively. The totaldownhole rate of production, q_(t), has been estimated, from theindividual oil and water rates at the standards conditions, withEquation (2) to feed the model.

TABLE 1 Parameters used in the segregated flow model q_(o) 2,000 STB/dk_(oz), k_(wz) 150 md μ_(o) 0.8 cP q_(w) 5,000 STB/d φ_(oz), φ_(wz) 0.15fraction μ_(w) 0.5 cP Water Cut 76% c_(r) 1.00E−06 psi⁻¹ C 0.05 bbl/psiS_(wirr) 0.15 fraction c_(o) 1.00E−05 psi⁻¹ s_(o) 0 dimensionlessS_(orw) 0.25 fraction c_(w) 3.00E−06 psi⁻¹ s_(w) 0 dimensionless k _(ro)1 fraction B_(o) 1.3 bbl/STB r_(w) 0.3 ft k _(rw) 0.75 fraction B_(w)1.0 bbl/STB p_(i) 5,000 psia H 150 ft

FIG. 5 shows the calculated flowing bottom-hole pressure for the entireduration. Individual phase rates 90 for oil and 92 for water, calculatedusing Equations (4) and (5), are also shown in FIG. 6 along with thetotal production rate 94. Pressure drop and pressure derivatives aredemonstrated in FIG. 7 for the buildup data. For the presented casestudy, oil phase flow capacity, computed using Equation (21), is 7,500md-ft, while water phase flow capacity, computed using Equation (22), is11,250 md-ft. The equivalent oil phase flow capacity, computed usingEquation (23), is 22,500 md-ft.

The present invention provides a new methodology where segregated flowis rigorously modeled as a two-layer reservoir system, based on theobserved physics. Thus, the applied mathematical model provides accurateestimates of the values of phase mobility of oil and water, in additionto the actual flow capacity of the formation. When more than onepressure-transient test is available at different water cut ratios,information about the end-point water relative permeability can beinferred. Average fluid saturations in the tested zone can also bedetermined with a reasonable accuracy. The present invention providesreliable reservoir characterizations and reserve estimations based onthe in-situ conditions of oil and water in the reservoir.

The present invention thus provides a practical application of theunderlying physics of multiphase flow under a segregated flow mechanism.The present invention provides a complete procedure to model segregatedflow conditions at various reservoir, fluid properties, water cut ratiosand wettability conditions.

The present invention captures the segregated flow mechanism as atwo-layer reservoir system, honoring the in-situ physics. Based onpetrophysical measurements (e.g., end-point relative permeability andend-point saturations), fluid properties (e.g., oil and waterviscosity), and geometry of individual phase zones (e.g., oil and waterzone thicknesses), an improved better description of the subsurfacesystems is provided, when formation oil and water fluids are flowingunder segregated multiphase-flow conditions. With the present invention,the multiphase flow parameters are explicitly defined, thus offeringaccurate physical representation of the actual conditions in thereservoir. The methodology utilizes oil and water zone thicknesses fromproduction-log measurements (also known as PLT in the industry), whichare widely used in the oil industry. If such information is notavailable, it can also be inferred from other source of data such as oiland water production rates as outlined above.

The present invention provides a more sophisticated representation ofthe underlying physics of segregated flow of oil and water through atwo-layer reservoir system. The present invention also handles fluidproperties data much more accurately than the Perrine method by uniquelydefining individual phase viscosity, instead of using pseudo-parametersto represent them. The Perrine approach is not flexible regardingincorporating data from the other sources, such as oil and waterthicknesses from production logs, and relative permeability end-pointdata. These parameters are taken into account with the present inventionfor a better reservoir description.

The invention has been sufficiently described so that a person withaverage knowledge in the field of reservoir modeling and simulation mayreproduce and obtain the results mentioned in the invention herein.Nonetheless, any skilled person in the field of technique, subject ofthe invention herein, may carry out modifications not described in therequest herein, to apply these modifications to a determined structureand methodology, or in the use and practice thereof, requires theclaimed matter in the following claims; such structures and processesshall be covered within the scope of the invention.

It should be noted and understood that there can be improvements andmodifications made of the present invention described in detail abovewithout departing from the spirit or scope of the invention as set forthin the accompanying claims.

1. Non-transitory computer readable storage medium comprising programinstructions stored thereon that are executable by a processor to causethe following operations for determining a measure of oil flow from anoil production zone in a layer of a subsurface reservoir and a measureof water phase flow capacity from a water production zone in the layerof the subsurface reservoir based on a pressure transient test ofproduction and pressure of the layer over time: obtaining production andpressure data for the layer over time from the pressure transient test,the production and pressure data comprising: for each sampled instant ofdifferent sampled instants of measurement during the pressure transienttest of the layer over time, a measure of well flowing pressure for thelayer; a measure of well pressure change for the layer over time duringthe pressure transient test of the layer; a pressure time derivative ofwell pressure for the layer at the given sampled instant of measurementduring the pressure transient test of the layer; fluid properties of thelayer including oil flow parameters for the oil production zone andwater flow parameters for the water production zone; and rock propertiesand geometrics of the layer; storing the production and pressure data ina database; (a) obtaining from the database the oil flow parameters forthe oil production zone and the water flow parameters for the waterproduction zone; (b) obtaining from the database the measure of wellflowing pressure for the layer at a given sampled instant of measurementduring the pressure transient test of the layer over time; (c) obtainingfrom the database the measure of well pressure change for the layer overtime during the pressure transient test of the layer; (d) obtaining fromthe database the pressure time derivative of well pressure for the layerat the given sampled instant of measurement during the pressuretransient test of the layer; (e) determining an estimate of oil phaseflow capacity of the oil production zone of the layer; (f) determiningan estimate of water phase flow capacity of the water production zone ofthe layer; (g) determining an estimated value of equivalent oil phaseflow capacity of the layer; (h) generating a model wellbore flowingpressure of the layer based on the measure of well flowing pressure ofthe layer at the given sampled instant of measurement during thepressure transient test of the layer over time obtained from thedatabase and the fluid properties of the layer; (i) generating a modelwell pressure change of the layer, based on the measure of well pressurechange of the layer over time during the pressure transient test of thelayer obtained from the database and the fluid properties of the layer;(j) generating a pressure time derivative of the model wellbore flowingpressure of the layer, based on the measure of pressure time derivativeof well pressure for the layer at the given sampled time instant ofmeasurement during the pressure transient test of the layer obtainedfrom the database and the model wellbore flowing pressure of the layergenerated; (k) generating a model oil production rate for the oil zoneof the layer based on the model wellbore flowing pressure of the layergenerated and the oil flow parameters for the oil production zone; (l)generating a model water production rate for the water zone of thelayer, based on the model wellbore flowing pressure of the layergenerated and the water flow parameters for the water production zone;(m) displaying, via an output display, the model wellbore flowingpressure of the layer generated, the model well pressure change of thelayer generated, the pressure time derivative of the model wellboreflowing pressure of the layer generated, the measure of well flowingpressure for the layer at the given sampled instant of measurementduring the pressure transient test of the layer over time obtained fromthe database, the measure of well pressure change for the layer overtime during the pressure transient test of the layer obtained from thedatabase, and the pressure time derivative of well pressure for thelayer at the given sampled instant of measurement during the pressuretransient test of the layer obtained from the database for: comparingthe model wellbore flowing pressure of the layer generated with themeasure of well flowing pressure for the layer at the given sampledinstant of measurement during the pressure transient test of the layerover time obtained from the database; comparing the model measure ofwell pressure change of the layer generated with the measure of wellpressure change for the layer over time during the pressure transienttest of the layer obtained from the database; and comparing the modelpressure derivative of the model wellbore flowing pressure of the layergenerated with the pressure derivative of well pressure for the layer atthe given sampled instant of measurement during the pressure transienttest of the layer; (n) receiving an indication of a match or anon-match, the match being indicative of the following conditions beingsatisfied, and the non-match being indicative of one or more of thefollowing conditions not being satisfied: (i) the model wellbore flowingpressure of the layer generated matches the measure of well flowingpressure for the layer at the given sampled instant of measurementduring the pressure transient test of the layer over time obtained fromthe database; (ii) the model measure of well pressure change of thelayer generated matches the measure of well pressure change for thelayer over time during the pressure transient test of the layer obtainedfrom the database; and (iii) the model pressure derivative of the modelwellbore flowing pressure of the layer generated matches the pressurederivative of well pressure for the layer at the given sampled instantof measurement during the pressure transient test of the layer, (o) inresponse to receiving an indication of a match, storing, in thedatabase, the model oil production rate for the oil zone of the layergenerated and the model water production rate for the water zone of thelayer generated; and (p) in response to receiving an indication of anon-match: adjusting values of the oil flow parameters for the oilproduction zone to generate adjusted oil flow parameters for the oilproduction zone and adjusting the water flow parameters for the waterproduction zone of the layer to generate adjusted water flow parametersfor the water production zone, and repeating steps (h) to (n) using theadjusted oil flow parameters for the oil production zone in place of theoil flow parameters for the oil production zone and using the adjustedwater flow parameters for the water production zone in place of thewater flow parameters for the water production zone, in response toreceiving an indication of a match at step (n) based on the adjusted oilflow parameters for the oil production zone and the adjusted water flowparameters for the water production zone, storing, in the database, thefollowing: the adjusted oil flow parameters for the oil production zone;the adjusted water flow parameters for the water production zone; themodel oil production rate for the oil zone of the layer generated basedon the adjusted oil flow parameters for the oil production zone and theadjusted water flow parameters for the water production zone; and themodel water production rate for the water zone of the layer generatedbased on the adjusted oil flow parameters for the oil production zoneand the adjusted water flow parameters for the water production zone. 2.The medium of claim 1, wherein the operations further comprise: formingan output display of the oil flow parameters for the oil production zoneand the water flow parameters for the water production zone of thelayer.
 3. The medium of claim 1, wherein the operations furthercomprise: forming an output display of the model oil production rate forthe oil production zone of the layer generated.
 4. The data storagedevice of claim 1, wherein the operations further comprise: forming anoutput display of the model water production rate for the waterproduction zone of the layer generated.
 5. The medium of claim 1,wherein the operations further comprise: forming measures of estimatedoil phase flow capacity for the oil production zone, water phase flowcapacity for the water production zone and equivalent oil phase flowcapacity of the layer.
 6. The medium of claim 5, wherein the operationsfurther comprise: forming an output display of the measures of theestimated oil phase flow capacity for the oil production zone, waterphase flow capacity for the water production zone and equivalent oilphase flow capacity of the layer.
 7. The medium of claim 1, wherein theoperations further comprise: forming a measure of estimated water phaseflow capacity for the water production zone.
 8. The medium of claim 7,wherein the operations further comprise: forming an output display ofthe measure of estimated water phase flow capacity for the waterproduction zone.
 9. The medium of claim 1, wherein the operationsfurther comprise: forming a measure of estimated equivalent oil phaseflow capacity of the layer.
 10. The medium of claim 9, wherein theoperations further comprise: forming an output display of the measure ofestimated equivalent oil phase flow capacity of the layer.
 11. Themedium of claim 1, wherein the operations further comprise: forming anoutput display of the adjusted oil flow parameters for the oilproduction zone and the adjusted water flow parameters for the waterproduction zone.
 12. The medium of claim 1, wherein the operationsfurther comprise storing the model wellbore flowing pressure of thelayer generated, the model wellbore pressure change of the layergenerated, and the model pressure derivative of the model wellboreflowing pressure of the layer generated.
 13. The medium of claim 12,wherein the operations further comprise forming an output display of themodel wellbore flowing pressure of the layer generated, the modelwellbore pressure change of the layer generated, and the model pressurederivative of the model wellbore flowing pressure of the layergenerated.
 14. The medium of claim 1, wherein the pressure transienttest is performed during well drawdown.
 15. The medium of claim 1,wherein the pressure transient test is performed during well buildup.